Landau-Zener treatments of solar neutrino oscillations

We present a simple derivation of the Landau-Zener formulas for nonadiabatic level crossings for linear and exponential density profiles. The derivation depends on a single assumption that applies somewhat differently to the exponential and linear cases, providing some insight into the relationship between the respective formulas. We note that one exponential Landau-Zener formula in common use is only approximately correct. Comparisons with exact calculations are made.